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How do I evaluate $$\int x^{x^x}\,\mathrm dx\ ?$$

I tried using integration by parts but couldn't do it. Please solve it for me. I found it in unsolved questions of maths calculus.

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  • $\begingroup$ Could you show us your efforts in solving the problem? $\endgroup$ – Chandler Watson Sep 5 '15 at 16:26
  • $\begingroup$ what do you exspect? $\endgroup$ – Dr. Sonnhard Graubner Sep 5 '15 at 16:28
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    $\begingroup$ Given the fact there does not exist a closed form for $\int x^x \mathrm{d}x$, it would amaze me if there is one for this one. $\endgroup$ – Nigel Overmars Sep 5 '15 at 16:29
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    $\begingroup$ It is an unsolved question because a closed form can't be found. $\endgroup$ – Siminore Sep 5 '15 at 16:30
  • $\begingroup$ Congratulations, this is now the Rahul function! $\endgroup$ – mickep Sep 5 '15 at 18:06
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There is no closed form for this according to Wolfram Alpha. That's probably why you found it on a list of open problems.

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    $\begingroup$ Beware, there are many answers on this site (and others) which produced closed forms to certain integrals, series and similar not exactly computable by Mathematica, Maple etc. $\endgroup$ – Vincenzo Oliva Sep 5 '15 at 17:15
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    $\begingroup$ @VincenzoOliva. This is a very, very good point you make here. Moreover, you did prove it today more than once. $\endgroup$ – Claude Leibovici Sep 5 '15 at 17:32
  • $\begingroup$ Wolfram alpha only says it cannot find a closed form. I think it is unlikely to indicate proof there is no closed form, but I could be mistaken. $\endgroup$ – Thomas Andrews Sep 5 '15 at 19:21

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